(a) Is it possible for an object to be in translational equilibrium (the first condition) but not in rotational equilibrium (the second condition)? Illustrate your answer with a simple example. (b) Can an object be in rotational equilibrium yet not in translational equilibrium? Justify your answer with a simple example.
Solution 2DQ The first condition of equilibrium states that the net force on a body is zero. The second condition states that the the net torque on the body is zero. (a) The body is said to be in translational equilibrium if it remains at rest. It has no tendency to accelerate as a whole. But the body may not be in rotational equilibrium if a net torque acts on it. Let us have a look at the following figure. Let us assume a spherical object as shown in the figure above. There is no unbalanced force acting on the same, hence it will remain at rest. But if two forces are applied on the object clockwise as shown above, then it will have a net clockwise torque about an axis of rotation passing through its center. Therefore, the sphere will not have any translational motion, but will have a rotational motion. Thus the first condition of equilibrium is satisfied, but not the second one. It is in translational equilibrium, but not in rotational equilibrium. (b) Yes, an object can be in rotational equilibrium,yet not in translational equilibrium. Rotational equilibrium means there will be no net torque on the object. Absence of translational equilibrium means that there will be a net force on the object. Let us have a look at the following figure to understand such a situation. Here, one of the forces is acting clockwise and the other is acting anticlockwise. Both are equal in magnitude. So, the net torque on the object will be zero as one will nullify the affect of the other. But since both the forces act along the same linear direction (upward) there will be a net force acting on the object. This force will cause the object’s translational motion. Thus we have seen that there may a rotational equilibrium associated with an object, yet it may not have translational equilibrium.